Warships were operated by the Time Lords, (AUDIO: Day of the Master) the Cybermen, (TV: Silver Nemesis) the warships (COMIC: Pureblood) and the Chula. (TV: The Empty Child)
In an account of the Last Great Time War in which the conflict was ended by the Eighth Doctor, concentric rings of Dalek warships surrounded the planet Gallifrey before they and the planet were destroyed by the Moment. (PROSE: Doctor Who and the Time War)
One of the largest Gallifreyan warships was the Starbane, which was capable of destroying entire galaxies. The Twelfth Doctor teamed up with a lone "good" Dalek to locate the Orb of Fates which served as the key to locating it. When they successfully retrieved all the fragments of the Orbs they found it already under Dalek occupation. The Doctor guided Lumpy through the Starbane and placed the Orb into the reactor which in turned destroyed the ship. (GAME: The Doctor and the Dalek)